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a(1)=2, a(n+1) is the smallest integer > a(n) such that the smallest prime factor of a(n+1) is the largest prime factor of a(n).
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%I #13 Mar 02 2015 18:06:27

%S 2,4,6,9,15,25,35,49,77,121,143,169,221,289,323,361,437,529,667,841,

%T 899,961,1147,1369,1517,1681,1763,1849,2021,2209,2491,2809,3127,3481,

%U 3599,3721,4087,4489,4757,5041,5183,5329,5767,6241,6557,6889,7387,7921

%N a(1)=2, a(n+1) is the smallest integer > a(n) such that the smallest prime factor of a(n+1) is the largest prime factor of a(n).

%H Harvey P. Dale, <a href="/A057602/b057602.txt">Table of n, a(n) for n = 1..1000</a>

%F Even numbered terms are squares of successive primes. Odd numbered terms are the product of two successive primes and are the square root of the product of the previous term and the next term - _Jud McCranie_, Oct 07 2000

%t Module[{nn=30,pr,ev,od},pr=Prime[Range[nn]];ev=pr^2;od=Times @@@ Partition[ pr,2,1];Join[{2},Riffle[ev,od]]] (* _Harvey P. Dale_, Mar 02 2015 *)

%Y Cf. A000040.

%Y A033476.

%K nonn

%O 1,1

%A _G. L. Honaker, Jr._, Oct 07 2000

%E Additional terms from _Jud McCranie_, Oct 07 2000